Atmospheric science component

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Journal of Wind Engineering

and Industrial Aerodynamics 93 (2005) 651–674

0167-6105/$ -

doi:10.1016/j

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State of Florida hurricane loss projection model:Atmospheric science component

Mark Powella,�, George Soukupa, Steve Cockeb,Sneh Gulatic, Nirva Morisseau-Leroyd, Shahid Hamidc,

Neal Dorsta, Lizabeth Axeb

aNOAA Hurricane Research Division, Miami, FL, USAbFlorida State University, Tallahassee, FL, USA

cFlorida International University, Miami, FL, USAdUniversity of Miami, Miami, FL, USA

Received 6 October 2003; received in revised form 25 April 2005; accepted 24 May 2005

Available online 22 July 2005

Abstract

The State of Florida has developed an open, public model for the purpose of probabilistic

assessment of risk to insured residential property associated with wind damage from

hurricanes. The model comprises atmospheric science, engineering, and financial/actuarial

components and is planned for submission to the Florida Commission on Hurricane Loss

Projection Methodology. The atmospheric component includes modeling the track and

intensity life cycle of each simulated hurricane within the Florida threat area. When a model

storm approaches within a damage threshold distance of a Florida zip code location, the wind

field is computed by a slab model of the hurricane boundary layer coupled with a surface layer

model based on the results of recent GPS sonde research. A time series of open terrain surface

winds is then computed for each zip code in the threatened area. Depending on wind direction,

an effective roughness length is assigned to each zip code based on the upstream fetch

roughness as determined from remotely sensed land cover/land use products. Based on

historical hurricane statistics, thousands of storms are simulated allowing determination of the

wind risk for all residential zip code locations in Florida. The wind risk information is then

see front matter Published by Elsevier Ltd.

.jweia.2005.05.008

nding author. Tel.: +1305 361 4403; fax: +1 305 361 4402.

dress: [email protected] (M. Powell).

www.elsevier.com/locate/jweia

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M. Powell et al. / J. Wind Eng. Ind. Aerodyn. 93 (2005) 651–674652

provided to the engineering and loss models to assess damage and average annual loss,

respectively.

Published by Elsevier Ltd.

Keywords: Hurricane; Risk; Insured loss; Damage; Catastrophe

1. Introduction

The historical record for establishing the risk of hurricanes throughout the coastalUnited States is limited to a period of about 100 years, with relatively reliable andcomplete records [1]. Unfortunately, this period is not sufficient to establish riskwithout large errors so alternative methods have been used since the 1970s [2,3].Hurricane risk models are currently used to conduct simulations of thousands ofyears of storms based on probability distributions of important historically observedparameters. This method is often referred to as the joint probability method since theprobability of having an event is coupled with the probability that the event is of agiven intensity. Commercial modeling interests have developed several versions ofthese which are used to advise the insurance industry for ratemaking. Unfortunately,the models are proprietary so customers whose rates have increased on the basis ofmodel calculations have no way of examining or questioning the results. The State ofFlorida is developing a public model to provide an understandable baseline forcomparison to the commercial models. The model will be open and transparent, inwhich methods and results can be examined in great detail. The Hurricane LossProjection Model consists (Fig. 1) of independent modules for atmospheric science,engineering, and actuarial components. Each component provides one-way input tothe next component in line until the end result (average annual loss per zip code) isachieved. This paper will describe the atmospheric science component of the model.

2. Threat area

To focus on storms capable of causing residential property damage in Florida, athreat area is defined to best capture the statistical characteristics of historicaltropical cyclones that have affected the state. The area within 1000 km of a location(26.0N, 82.0W) off the southwest coast of Florida (Fig. 2) was chosen since thiscaptures storms that can affect the panhandle, west, and northeast coasts of Florida,as well as storms that approach South Florida from the vicinity of Cuba and theBahamas. A model flow chart (Fig. 3) describes the order of calculations for theatmospheric science component.

3. Annual occurrence

The model has the capability of simulating climate cycles and tropical cycloneactivity according to different periods of the historical record [4]. The historical record

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Atmospheric Science Component IStorm genesis

MovementIntensity

Atmospheric Science Component IIWind Field

Zip Code time seriesTerrain influences

Probabilities of exceedence

Engineering ComponentInventory of residential construction Damage when wind load exceeds

resistance

Financial/Actuarial ComponentCompute insured losses

Average annual loss by zip code

State of Florida Hurricane Loss Projection Model

Fig. 1. Flow chart depiction of independent modules of the State of Florida Hurricane Loss Projection

Model.

M. Powell et al. / J. Wind Eng. Ind. Aerodyn. 93 (2005) 651–674 653

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1000 kmFLORIDAHURRICANETHREAT AREA

Fig. 2. Threat area map. All storms entering or developing within the threat area are considered for

characteristics relating to formation, movement, and intensity.


for the Atlantic tropical cyclone basin (known as ‘‘HURDAT’’) is a six hourly recordof tropical storm and hurricane positions and intensities [5], which are expressed asestimated maximum 1min surface (10m) winds and, when available, central sea levelpressure. The period 1851–2004 is the largest available, but the period 1900–2004 ismost often used due to uncertainties about 19th century storms, especially for Florida,due to a lack of population centers and meteorological measurements of hurricanesbefore the start of the 20th century. There are also uncertainties about the first half ofthe 20th century since aircraft reconnaissance only began in the 1940s so anotherchoice in the period of record are the years 1944–2004. Four additional choices areavailable which simulate the warm (El Nino, fewer hurricanes) and neutral or cold (LaNina, more hurricanes) inter annual climate cycles in tropical cyclone activity, as wellas the cold or warm phases of the Multi-decadal climate cycles. These choices areprimarily for research purposes and constrain the historical record to use only yearswith the specified climate cycle to fit annual tropical cyclone occurrence. For insuranceapplications the 1900-prior year period will be of most interest (e.g. for the 2005season, the period 1900–2004 would be of interest if the 2004 season official hurricanetracks are available). Two fits are tested to the annual hurricane occurrence frequencydistribution: the negative binomial and the Poisson model. Chi-square goodness of fittests determine which fit is used for the subsequent simulations. The chosen fit is thenrandomly sampled to determine how many storms occur for each year of thesimulation. Once the number of tropical cyclones within the threat area for a givenyear is determined, the date and time of genesis is computed from an empiricaldistribution based on historical storm tracks.

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Select number of storms per year from PDF of annual hurricane occurrence rate

Select number of years for simulation

Select genesis time and location of each storm from temporal and geographical PDFs

Model storm track and intensity at 1h intervals using geographic motion and intensity change PDFs

Every 15 min, compute open terrain wind speed and direction at all zip codes within damage threshold distance of storm center

Determine wind model parameters for all Florida hurricane landfalls: Delta P, Rmax, Storm speed, Pressure profile

Correct winds to actual terrain based on upstream fetch and roughness

State of Florida Hurricane Loss Projection ModelAtmospheric Science Component

Determine wind speed exceedance probabilities at each zip code

Compute damages at each zip code: Engineering damage model

Compute average annual loss:Actuarial loss model

Fig. 3. Flow chart depiction of the atmospheric science component of the State of Florida Hurricane Loss

Projection Model.


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4. Storm genesis, movement, and intensity

The threat area is divided into regions that contain the historical and seasonalcharacteristics of storm motion and intensity change. Initial location, intensity, andmotion for each storm are based on the geographic probability distributions of eachquantity for a given time within the season. Intensity is initially modeled as thegradient of pressure Dp, the difference between the central minimum sea levelpressure and an outer peripheral pressure (assumed to be 1013 hPa). Ultimately(after the wind model is run) the intensity is defined according to the maximumsurface wind speed in the storm. Hurricane tracks are modeled as a Markov process.We use a stochastic approach to model the storm genesis location and track andcentral pressure evolution. A probability distribution function (PDF) for the initialstorm position is derived from the historical ‘‘genesis’’ data. Here, we define genesisas the time when a hurricane forms in or first appears in the threat area. The PDF isderived for 0.51 latitude/longitude box regions, as well as time of season (month). A(uniform) random error term is added so that the storm may form anywhere withinthe 0.51 box. Fig. 4 shows a plot of the spatial PDF for storm genesis locations in thethreat area for the month of August.

We derive discrete PDFs based on historical data to provide the initial andsubsequent motion and intensity of the storm. A storm is simulated byrepeatedly sampling from these PDFs via a Monte Carlo approach. These PDFsare derived for variable-sized regions centered at every 0.51 latitude and longitude inthe hurricane basin. The size of these regions is determined to be that which gives arobust probability density function (PDF) for the quantities of interest (speed,direction, and central pressure), up to some maximum size. Once the storm has beengiven an initial condition, its subsequent evolution is governed by sampling thePDFs for changes in intensity, translation speed, and heading angle in 1-hincrements.

Intensity change is modeled by using the observed geographic probabilitydistribution of 6-h changes of central pressure as related to the relative intensity, ameasure of how close the storm comes to meeting its maximum possibleintensity (potential intensity) [6]. Potential intensity takes into account theconcept of the hurricane as a heat engine constrained by the input (sea surface)and outflow (upper troposphere) temperatures. Intensity change is limited so as tonot exceed the maximum observed change for a particular geographic region. Whena storm center crosses the coastline (landfall) the intensity change follows a pressuredecay model (discussed below). If the storm moves back over the sea, the formerintensity change model is reinstated. A storm need not make landfall to beconsidered however; bypassing hurricanes are considered that never make landfall,or make landfall well before or well after producing damaging winds at a particularzip code.

The PDFs for change in storm translation speed and direction depend on thecurrent speed and direction (binned in discrete intervals), as well as geographiclocation (0.51 lat-lon location) and time of season (month). Fig. 5 shows a PDF forchange in direction for eight possible direction intervals (451 intervals). The PDF

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39N

36N

33N

30N

27N

24N

21N

18N

15N

12N

93W 90W 87W 84W 81W 78W 75W 72W 69W 66W

0.06

0.055

0.05

0.045

0.04

0.035

0.03

0.025

0.02

0.015

0.01

0.005

Fig. 4. Geographic distribution of probability of a storm entering or developing within the threat area

during the month of August based on the historical period 1900–2000.

-40 -30 -20 -10 0 10 20 30 40Change in Direction

0

0.2

0.4

0.6

0.8

Prob

abili

ty

Probability of Change in Directionfor 8 current direction intervals

0-4545-9090-135135-180180-225225-270270-315315-360

Fig. 5. Probability of a change in direction of storm motion (over a 6 h time period) to the left or right of

the current motion as a function of the current storm heading (in degrees from north).


indicates that the storm has a high probability for maintaining current direction,except for westward traveling storms which tend to turn right (northward)somewhat.

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Our approach has a great advantage over early models [2,3] that considered acircular approach region surrounding coastal cities. Storms that parallel the coast ormake several landfalls can be properly simulated with our method.

5. Storm decay

The tropical ocean is typically warmer than the air above it, enabling a transfer ofheat and moisture to the air. Inflow towards the center of the tropical cyclonetransports this energy toward the eyewall, where it can help sustain convection,leading to a positive feedback of warming in the eye, lower minimum centralpressure, stronger inflow, and more energy transport [7,8]. Over the ocean thispositive feedback loop may be slowed or reversed by ocean cooling, advection ofrelatively cold dry air with a history of travel over land, or strong wind shear thatprevents the storm center from focusing heating in the eye [9,10]. As a hurricanemakes landfall, the circulation traverses land, and the storm loses its source of energy[11]. More and more dry and relatively cool air flows towards the center, causing theair to cool as it expands adiabatically while approaching lower pressures [12]. Theresult is that the eye heating gradually decreases and the central pressure begins toincrease or ‘‘fill’’.

Since the wind model depends on the specification of the pressure gradient, amethod was needed to estimate the central pressure over land. As a starting point fora simple decay model we will use the exponential decay as a function of time afterlandfall developed by Vickery and Twisdale [13]. The HURDAT database and Hoet al. [14] contains documentation of storm decay and pressure filling for manyhurricane landfall cases in the historical record. Vickery and Twisdale [13] developedand tested a model for the Florida peninsula based on nine landfalling hurricanesand found the model to be slightly conservative (larger values) within 3 h of landfalland slightly non-conservative (smaller values) beyond 3 h after landfall. The form ofthe model is

DpðtÞ ¼ Dp0 expð�atÞ, (1)

where Dp(t) is the time-dependent central pressure deficit and t represents the timeafter landfall. The filling rate constant is given as

a ¼ a0 þ a1Dp0 þ �, (2)

where e is a random error term with a normal distribution. The dependence of thefilling rate constant on Dp0 allows stronger storms to decay faster than weak storms;a characteristic observed in hurricane landfalls [15]. The random error term allowsfor the possibility that some storms will decay slower or faster than average. For theFlorida peninsula Vickery and Twisdale [13] use a0 ¼ 0.006, a1 ¼ 0.00046, and thestandard deviation of 0.0025.

The Kaplan and DeMaria [16] model is also pertinent but it deals with wind decayrather than pressure decay and there is no well-established method to convert inland-decayed peak winds to central pressure. The advantage of the filling model is that it

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provides a starting point to invoke an intensity redevelopment for storms that exitthe coastline and re-intensify over water. When a storm reemerges over water, theintensity is modeled along the track the same way it was before landfall using thedecayed pressure as an initial value.

6. Damage distance threshold

To save computing resources, the wind field is not evaluated unless a hurricanepasses within a distance from the storm at which damage might be possible, thedamage distance threshold. Hurricanes come in a variety of sizes and shapes, so afixed distance criterion may not be practical, since it may be unnecessarily large forsmall storms. As an alternative, we describe the damage distance threshold (D) as afunction of the radius of maximum wind speed (Rmax). For small storms with smallRmax we will go outward from the storm center �10 Rmax and for large storms wewill go out a as far as 4 Rmax.

Twelve hurricanes comprising a variety of storm structures and shapes wereevaluated by comparing HRD Hurricane Wind Analysis System (H�Wind) analysesof the outermost radius of marine exposure 25m/s sustained winds. For hurricaneswith Rmax450 km, D is held constant at 4 Rmax. For Rmaxo48 km,

D ¼ 12:323� 0:162Rmax. (3)

The 25m/s sustained marine wind speed contour represents a 1 h mean marine windof 21m/s. This wind speed is assumed to represent the mean marine exposure windspeed at which light damage begins. The equivalent 1 h mean wind for roughnessrepresentative of Florida zip codes is �14.5m/s.

7. Wind field model

The model is based on the slab boundary layer concept originally conceived byOoyama [17] and implemented by Shapiro [18]. Similar models based on thisconcept have been developed by Thompson and Cardone [19] and Vickery et al.[20,21]. As in Ref. [18], the model is initialized by a boundary layer vortex ingradient balance. Gradient balance represents a circular flow caused by thebalance of forces whereby the inward directed pressure gradient force is balancedby outward Coriolis and centripetal accelerations. The coordinate system trans-lates with the hurricane vortex moving at velocity ~c. The vortex transla-tion is assumed to equal the geostrophic flow associated with the large-scale pressure gradient. As a possible future enhancement the large-scale flow inwhich the vortex is embedded may be treated independently of the vortex motionas in Ref. [19]. In cylindrical coordinates that translate with the moving vortex,equations for a slab hurricane boundary layer under a prescribed pressure

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gradient [18] are

uqu

qr�

v2

r� fv þ

v

r

qu

qfþ

qp

qr� K r2u �

u

r2�

2

r2qu

qf

� �þ F ~c; uð Þ ¼ 0 ¼

qu

qt, (4)

uqv

qrþ

v

r

� �þ fu þ

v

r

qv

qf� K r2v �

v

r2þ

2

r2qu

qf

� �þ F ~c; vð Þ ¼ 0 ¼

qv

qt, (5)

where u and v are the respective radial and tangential wind components relative tothe moving storm, p is the sea-level pressure which varies with radius (r), f is theCoriolis parameter which varies with latitude, f is the azimuthal coordinate, K is theeddy diffusion coefficient, and F(c,u), F(c,v) are frictional drag terms (discussedbelow). All terms are assumed to be representative of means through the boundarylayer. The motion of the vortex is determined by the modeled storm track.

Note that Eqs. (4) and (5) represent a steady-state solution. In order to solve theequations, they must be integrated until the steady state assumption is satisfied eitherthrough time integration (e.g., see Refs. [18,19]) or numerical method (see AppendixA). More sophisticated multiple level models (e.g., see Ref. [22]) include equationsdescribing the thermodynamic processes including convection, cloud and precipita-tion microphysics, evaporation of sea spray, exchange of heat and moisture with thesea, etc. These processes interact to change the pressure and wind fields over time,but the computational requirements of such models make them poorly suited for riskassessment. An advantage of our approach is that the solution to (4) and (5) isstraightforward and we do not have the computationally costly requirement to runthe model to ‘‘steady state’’ each time we desire a solution. A limitation of our model(and all other Hurricane risk models) is the lack of physical representation ofadditional processes that may influence the wind field of a tropical cyclone.

7.1. Surface pressure field

The symmetric pressure field p(r) is specified as

pðrÞ ¼ p0 þ Dpe Rmax=rð ÞB

(6)

where p0 is the central minimum sea level pressure, B is the Holland [23] pressureprofile shape parameter, R is the radius of maximum wind speed (in nautical miles),and Dp is the pressure deficit defined earlier. The central pressure is modeledaccording to the intensity modeling in concert with the storm track.

The mean tangential gradient wind is determined primarily by (6). A recentpublication by Willoughby and Rahn [24] of the NOAA-HRD database of researchand reconnaissance aircraft measurements was supplemented with central pressuremeasurements and Rmax values adjusted for tilt between the surface and the 3 kmlevel. These data were then cut to be more relevant to our model. We retained 201profiles with maximum winds 433m/s, with flight levels below the 700 hPa pressuresurface, and with Atlantic basin latitudes 15–35N and longitudes west of 601 West.The resulting expression for B explains 20% of the variance:

B ¼ 1:881093� 0:010917 Lat� 0:005567 Rmax þ �, (7)

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where Lat is the latitude and e is a random term from a zero mean normaldistribution with a standard deviation of 0.286. B is censored to remain above 0.8and below 2.2.

7.2. Radius of maximum wind

The radius of maximum wind is determined from a distribution of landfall valuesas a function of p0 and latitude. As in Ref. [21], a log normal distribution is assumedfor Rmax with a mean value determined as a function of p and latitude. In developingthe models for Rmax, we used the data from Ref. [14] for storms from 1900 to 1983;NOAA-HRD archives of realtime surface wind analyses from 1995 to 2002; an‘‘extended best track’’ archive of the National Hurricane Center that was maintainedby Dr. Mark DeMaria [25] (now with NOAAs NESDIS at Colorado StateUniversity) for the years 1988–1999; and an HRD archive of aircraft observationsfor the years 1984–1987. To create a model to describe Rmax we considered Gulf ofMexico and US Atlantic coast hurricane landfalls with latitudes as high as 341 Northin order to help fill a dearth of information on storms affecting the NortheastFlorida coastline. The relationship between Rmax and p and latitude shows muchscatter but a generalized linear model for the natural log of Rmax (r2 ¼ 0.212)provides a useful estimation:

ln Rmax ¼ 2:0633þ 0:0182Dp � 0:00019008Dp2 þ 0:0007336Lat2 þ �, (8)

where e is a normal random variable with a mean of zero and a standard deviation of0.3. Eq. (7) describes the mean of the log normal distribution of Rmax in nauticalmiles. When a simulated storm is close enough to land to become a threat, an Rmax

value is randomly chosen given the p and latitude. Rmax is computed at each timestep but the random error term is computed only once for each landfall. Rmax iscensored to remain below 102 km and above 7.4 km.

7.3. Friction terms

The frictional drag is in the direction opposite the total wind relative to the earthat the surface and represents the mean momentum flux from the atmosphere to thesurface. The frictional terms in (3) and (4) may be specified in terms of the verticalgradient of stress:

F ~c; uð Þ ¼qtqz

. (9)

The variation of t with height over the depth of the slab boundary layer may bedescribed by a function with properties supported by observations in the surfacelayer of tropical cyclones. The lower 250m of the boundary layer is occupied by asurface layer in which stress is approximately constant. In reality, the stress isgreatest close to the surface, and is zero at the top of the boundary layer. Byassuming stress as near constant over the surface layer we satisfy conditions forapplying the logarithmic wind profile to describe the vertical variation of the mean

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wind speed with height. The fact that a mean logarithmic wind profile has beenobserved in tropical cyclone eyewalls [26] provides justification for the surface layerconcept. The evaluation of (9) is approximated as 0.25 (tsfc/h), where tsfc is thesurface stress and h represents the top of the boundary layer. Based on the meanheight of the wind maximum in the hurricane eyewall in [26], an h value of 500m isjustified. The factor 0.25 is based on judgment and takes into account the fact thatthe average stress in the slab boundary layer is less than the mean stress of thesurface layer. This factor is consistent with preliminary calculations of the stressprofile in the boundary layer derived from GPS sonde observations described in [26].Other modelers using the slab boundary layer approach have used 0.3 [13] and 1.0[18]. At the surface, the stress may be expressed in terms of the earth-relative surfacewind velocity U10 at a height of 10m above the surface, and the neutral stabilitysurface drag coefficient, Cd:

tsfc ¼ rCd~U10 þ~c ~U10 þ~c

� �� , (10)

F c; uð Þ ¼qtqz

¼ 0:25th, (11)

where Cd is specified by Large and Pond [27] and U10 is the neutral stability surface(10m, 32 ft) wind speed relative to the moving storm.

7.4. Eddy diffusion

The wind model describes the effects of horizontal turbulence following Shapiro[18]. In theory the role of eddy diffusion is to represent horizontal turbulent mixingin the radial and tangential directions. Vertical turbulent mixing (contained in thefriction terms discussed earlier) is typically much larger in magnitude and isassociated with a large body of research based on numerous field investigations.Horizontal mixing is most prominent in regions with strong horizontal gradients.Hence, the greatest impact of eddy mixing will be in the eyewall where radialgradients are strong. In practice, this term primarily serves as a way to smooth outcomputational noise in the model results but future enhancements might include adependence on horizontal shear or grid spacing.

7.5. Model implementation

The hurricane wind field model is based on a fully two dimensional, time-independent, scaled version of the tangential and radial momentum equations (4)and (5) for the mean boundary layer wind components (see Appendix A for acomplete description). The model makes use of a polar coordinate representationgrid centered on the moving cyclone. The nested circles are separated from theirinscribed and circumscribed neighbors by a radial separation of 0.1 R/Rmax; theazimuthal interval of the radial spokes is 101.

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6

4

2

2 4 6

0

0

-2

-2

-4

-4-6

-6

EARTH RELATIVE TOTAL WINDS (M/S) … c=5 m/s

Fig. 6. Horizontal distribution of mean surface wind speed, relative to a storm moving northward at

5m/s. Horizontal coordinates are scaled by the radius of maximum wind.


Implementation proceeds according to the following steps: First, based on theinput parameters, Rmax, p0, and B, radial profiles of the radial and tangential windsare calculated based on a stationary cyclone over open water to provide an‘‘envelope’’ with which to set the size of the cyclone vortex. The wind field producedby these profiles is radially symmetric.

Azimuthal variation is introduced through the use of two form factors. The formfactors multiply the radial and tangential profiles described above and provide a‘‘factorized’’ ansatz for both the radial and tangential storm-relative windcomponents. Each form factor contains three constant coefficients which arevariationally determined in such a way that the ansatz constructed satisfies (as far asits numerical degrees of freedom permit) the scaled momentum equations for thestorm-relative polar wind components. The azimuthal variable (f) has its usualmathematical meaning such that increases from left to right with the rectangularX-axis aligned ( ¼ 180, 0) and the Y-axis aligned ( ¼ 270, 90) with Y increasing in thedirection of storm translation.

The storm translation vector is added to the storm-relative wind components inorder to obtain the earth-relative wind field. The translational motion of the storm isincorporated in the surface friction terms in the momentum equations which dependon the and are specific for the direction of storm translation which is aligned with theY-axis. The wind field grid is then rotated so that the computational Y-axis coincideswith the actual direction of motion of the cyclone center. The wind field thus far

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constructed (Fig. 6) usually shows the location of peak winds to be to the right orforward edge of the right-rear quadrant of the cyclone.

7.6. Asymmetries in the wind field

The solution of (4) and (5) exhibits a shift of the radius of maximum winds towardthe center when compared with the gradient wind profile. The tangential winds arealso super gradient due to the advection inward of angular momentum induced bythe frictional convergence. Besides vortex translation, radial advection of tangentialmomentum, and differential friction, other factors affecting the asymmetricdistribution of winds in a tropical cyclone include synoptic scale vertical shear ofthe horizontal wind, synoptic scale weather features (e.g. a strong high pressure ridgeto one side of the hurricane), rain band convection, concentric eyewall cycles,mesoscale variations in air-sea temperature difference, and tertiary circulationsassociated organized linear flow features and turbulent eddies. In the simple modeldescribed here, only the motion and differential friction influences are taken intoaccount. The remaining features are difficult to parameterize and may becomputationally prohibitive to include in the model but play an important role indetermining the azimuthal location of the peak wind. Future versions of the modelwill attempt to include enhancements that take into account asymmetric wind fieldmechanisms.

7.7. Marine surface layer

Once the mean PBL motion field is determined, the surface wind isestimated through surface layer modeling. Monin-Obukov heights provide anestimate of the importance of shear- or mechanically produced turbulence tobuoyancy-produced turbulence. The large values of Monin-Obukov heightscomputed in tropical cyclones by Moss and Rosenthal [28] and Powell [29] areconsistent with shear-induced turbulence associated with neutral, well-mixedsurface layers. Hence, a neutral stability surface layer is assumed to exist. Inthese conditions we can specify the surface stress and friction velocity in terms of adrag coefficient, and use the well-known log profile to describe the variation ofwind speed with height. The mean boundary layer (MBL) depth is assumed to be500m, and the MBL wind speed is assumed to apply to the midpoint of this layeror 250m. The MBL height assumption is consistent with mean GPS sonde windspeed profiles [26] which depict the maximum winds at 500m. A log profilefor neutral stability is assumed to apply from the surface (10m) to 250m.Recent research on marine boundary layer wind profiles in tropical cyclones [26]supports this assumption to at least 150m. The mean surface wind for marineexposure is assumed to be 80% of the slab boundary layer wind, in accordancewith recent results from boundary layer wind profiles measured in tropical cyclones(Ref. [26]):

~U10

�� 0:8 Vj j. (12)

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There is considerable variability in the factor used to estimate the mean surface windspeed. The standard deviation of the reduction factor in (12) is about 10% but this isfurther complicated by profile failures in extreme conditions and the fact that theprofiles are representative of open ocean conditions, rather than coastal onshoreflow. When sufficient eyewall wind profiles become available near the coast, it isconceivable that a more sophisticated approach would involve sampling from astatistical distribution of coastal marine boundary layer reduction factors. Theheight of the model surface wind is 10m in accordance with the American Society forTesting and Materials (ASTM) standard practice for characterizing surface wind [30]and is assumed to represent a mean over a 1 h time period [13]. We should note thatthe appropriate time period to assign the model wind speed is not well known andcould be adjusted based on how well the model compares to observations. Otherhurricane risk models assign wind speed averaging time periods of 20–60min (seeRefs. [13,19]), while real-time hurricane wind analyses using surface winds estimatedwith model-adjusted flight-level or GPS sonde MBL measurements typically assume5–10min averaging periods.

Marine roughness is modeled using the Large and Pond [27] drag coefficient (10)to compute friction velocity given the mean surface wind speed, and then solving theneutral stability log law for Z0. The Large and Pond [27] expression for dragcoefficient was found to compare well with open-ocean measurements in hurricanes

Fig. 7. Dependence of coastal roughness on maximum 1min sustained wind speed for onshore flow.

Preliminary measurements from Cape Hatteras in the eyewall of Hurricane Isabel, courtesy of the State of

Florida Coastal Monitoring Program. Isabel measurements [29], from 5m (squares), 10m (x), profile

method (triangle), Large and Pond’s [27] drag coefficient relationship (diamonds), and open ocean [23]

measurements from other hurricanes (Y).

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for wind speeds up to hurricane force. For higher wind speeds, recent hurricanemeasurements [26] suggest that the drag coefficient and roughness decrease withwind speed over the open ocean. However, sea state conditions during the landfall ofa hurricane are very different from those over the open ocean. Anctil and Donelan[31] suggest that shoaling conditions in the shallow water adjacent to the coastlinecause increased roughness and drag coefficient. An extrapolation of the Large andPond [27] expression to hurricane wind speeds yields Cd values larger than thoseobserved over the open ocean. This behavior is consistent with additional surfacelayer turbulence associated with coastal wave breaking and shoaling conditions.Further justification for our approach comes from preliminary results of coastalroughness measurements within 200m of the shore recently obtained during thelandfall of Hurricane Isabel at Cape Hatteras by the State of Florida CoastalMonitoring Program [32]. These unique measurements (Fig. 7) in onshore flowdocument roughness values measured by the turbulent intensity method at 5 and10m heights, in addition to the profile method. Although there is considerablescatter among the different methods, the results are consistent with the Large andPond [27] estimates and more than an order of magnitude larger than open-oceanroughness [26] in similar wind speeds. Further measurements are needed to see if thisbehavior persists for winds greater than a Saffir–Simpson category one hurricane,and for onshore flow without possible effects of intervening dunes.

8. Land friction influences

To standardize observations for a common terrain [33], the mean surface wind formarine conditions is converted to ‘‘open terrain’’ conditions over land using theexpression given in Simiu and Scanlan [34]. Improved techniques for convertingbetween large and small roughness regimes are the subject of a future modelenhancement. For each 10min segment of storm motion, the open terrain exposuresurface wind speed and direction is determined for all population-weighted zip codecentroid locations within the damage threshold distance from the storm center. Theopen terrain wind at each zip code centroid is corrected to the observed terrain usinga fetch-dependent effective roughness for that particular direction and zip code. Theeffective roughness takes into account the flow over upstream flow obstacles andassumes that internal boundary layer development prevents the flow from reachingcomplete equilibrium with its surroundings [33,35]. The flow is most influenced bythe roughness of the terrain 3 km upstream of the zip code centroid, but the flow isstill influenced by terrain further upstream. The approach we use is based on theSource Area Model (SAM) described in Schmidt and Oke [36] and implemented byAxe [37]. SAM takes into account turbulence created by patchy terrain anddetermines the relative importance of the turbulence source area on a downstreamwind sensor located at the zip code centroid. This approach is an improvement overcurrent models that consider zip code roughness constant for all wind directions.Our method is especially advantageous for coastal zip code locations since flow withan upstream fetch over the sea can be significantly stronger than flow over a constant

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Fig. 8. Distribution of aerodynamic roughness (m) for the State of Florida determined from multi-

resolution land-use land-cover classifications.


land roughness. The geographic distribution of roughness (Fig. 8) is associated witha classification of the land use/land cover (LU/LC) in a particular region accordingto high resolution (50m) LANDSAT imagery used to develop the National Multi-Resolution Land Cover database [38]. Determination of the roughness for each LU/LC classification was developed by the National Institute for Building Sciences forFEMA’s multi hazard damage mitigation model (HAZUS). A limitation of the LU/LC method is that only 21 classifications are available with only two correspondingto developed residential areas. Florida Water Management District LU/LCdatabases include additional classifications but only three residential classifications.Detailed analysis of airborne lidar data is expected to provide more accuratedistributions of surface roughness in the future.

A gust factor [33,39] is used to convert the mean surface wind for the appropriatefetch-dependent roughness to a maximum sustained one min wind as required by theState of Florida Commission on Hurricane Loss Projection, and to a peak 3 s gust asrequired for the engineering component damage calculations. The same effectiveroughness is used for the mean wind and gusts. We should caution that theequilibrium fetch lengths for gusts and mean winds are not the same and a moresophisticated fetch modeling approach may be needed to address this in the future.An example of the model wind field for three 2004 hurricanes affecting FloridaHurricane are shown in Fig. 9. At the end of a simulation, time series of wind speedand direction exist for all zip codes in Florida for which hurricanes (or hurricanesthat have decayed to a weaker status) have passed within the damage thresholddistance. An advantage of our approach over other models is that the complete timeseries of the wind may be retained at high resolution. Retaining this informationmakes possible the determination of additional damage-relevant parameters such as

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Fig. 9. Comparisons of model surface wind field to observation based H�Wind analyses of 2004

Hurricanes Charley, Frances, and Ivan. Wind fields represent maximum sustained (1min) surface wind

speeds (m/s) for marine exposure. Scaled horizontal coordinate is R/Rmax, North is at top of figure.


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duration of winds exceeding hurricane force and wind steadiness. Powell et al. [40]showed that the highest damage observed in Hurricane Andrew was associated withlarge values of duration and small values of wind direction steadiness. Theseparameters capture the physical torques of thousands of gust-lull cycles acting on astructure. In addition, given the susceptibility of residential buildings to damage atroof corners and gables, the more the wind direction changes during a strong windevent, the greater the chance that a given wind direction will occur for which astructure is susceptible. Currently the time series capability is available only forscenario simulations. A future enhancement of the model will relate the duration andwind direction unsteadiness to the vulnerability functions contained in theengineering damage component of the model.

9. Validation and certification

The track and intensity model will be validated by comparison to historicaldistributions of landfalls by intensity, translation speed, and Saffir–Simpsoncategory along the Florida coastline. The wind model accuracy will be validatedby statistics of grid point comparisons of model fields to observation-based windfield analyses (Fig. 9) as well as to wind speed and direction time series measurementsat selected locations. The model is scheduled for submission in 2005 to the State ofFlorida Commission on Hurricane Wind Loss Projection [41]. The submissionprocess involves satisfying a rigorous set of published standards and providingrequired disclosures. Independent review of all model components are necessarybefore submission. A second review is completed on-site by a team of professionalswho report to the Commission. Finally the Commission will formally review themodel. A positive result will certify the model for use in Florida.

10. Conclusions

A Monte Carlo simulation model has been constructed to estimate average annualloss from hurricane wind damage to residential properties. The model is open in thesense that all results will be accessible to the public and the methodology will becompletely documented and available for examination. The model incorporatesresults of many recent research advances while keeping it basic enough to run in areasonable amount of time. In order to reduce sampling error, a very largesimulation (�50,000–100,000 years of activity) is prescribed. It is expected that themodel would be run once per year to take advantage of the latest historical data toassess annual wind exceedance probabilities at each zip code in Florida. Suchinformation can then be provided to the engineering and actuarial components of themodel to assess average annual loss for any given residential property exposureportfolio. At present, the wind model calculation requires minutes of computationtime per storm, requiring the simulations to be distributed among a number ofpowerful workstations. The primary user will be the Florida Department of

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Financial Services, insurance companies, and homeowners in the state of Florida.There are also many research uses for the model and it is expected that annualenhancements will be required to keep up with the state of the art. The model willreside at Florida International University’s International Hurricane Research Centerin Miami. Complete documentation of the model algorithms and code will beavailable for public examination. Given that there may be one Florida hurricanelandfall per simulation year, a large number of storms will be contained in ourdatabase. Each storm may effect as many as 50 zip codes so it is expected that thedatabase could contain several million records for track, intensity, and landfall windfield information on each storm. The database could then be queried for details onsimulated storms and wind exceedance probability distributions relevant to a givenzip code or county in Florida.

Acknowledgments

This research is supported by the State of Florida through a Department ofFinancial Services grant to the Florida International University InternationalHurricane Research Center. We thank the Department of Homeland Security(Federal Emergency Management Agency) and the National Institute for BuildingSciences for their assistance with the roughness classifications. Dr. Chris Landsea ofNOAA-AOML provided the climate cycle information used for the annual hurricaneoccurrence portion of the model. We appreciate helpful comments by Drs. RobertRogers, Matthew Eastin, Chris Landsea, and the anonymous reviewers.

Appendix A. Hurricane model equations and integration

A.1. Definitions

rmax
radius of maximum surface wind speed, specified ct storm translation speed, specified from storm track cdir storm translation direction compass heading,
specified from storm track
Dp central pressure deficit, specified
pðrÞ ¼ p0 þ Dpe� rmax=rð ÞB
sea level pressure
B
Holland profile parameter f Azimuthal coordinate, measured counterclockwise
from east
s ¼ r/Rmax normalized radial coordinate vg(s) Gradient wind: v2g=s þ rmaxfvg ¼ ð1=rÞ ðqp=qsÞ
f ¼ 2O sinY
Coriolis parameter Y latitude of storm center

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O
earth angular acceleration v0(s) normalized gradient wind (symmetric) ¼ vg(s)/
vgmax, where vgmax is the maximum gradient wind inthe radial profile

f̄ ¼ rmaxf =vgmax
normalized Coriolis parameter
vðs;fÞ ¼ v=vgmax
normalized storm-relative tangential windcomponent
uðs;fÞ ¼ u=vgmax
normalized storm-relative radial wind component
a
friction coefficient, rmaxCd=h
h
mean boundary layer height Cd drag coefficient c ¼ ct=vgmax normalized translation speed
gðsÞ ¼ 2v0ðsÞs�1 þ f̄ , (A.1)

dðsÞ ¼ _v0 þ v0s�1 þ f̄ , (A.2)

where a ‘‘dot’’ represents a derivative with respect to s, g(s) and d(s) depend only onv0 and f̄ sðs;fÞ ¼ vðs;fÞ � v0ðsÞ normalized departure from gradient balance.

A.2. Scaling of the governing equations prior to implementation

Substituting the terms from the above definitions and changing the radialcoordinate from r to s, the steady-state form of the governing equations (4) and (5)become:

uqsu þ s�1ðv0 þ sÞqfu � sðg þ s�1sÞ þ aðu þ c sin fÞðw � cÞ ¼ 0, (A.3)

uqssþ s�1ðv0 þ sÞqfsþ uðd þ s�1sÞ þ aðv0 þ sþ c cos fÞðw � cÞ ¼ 0, (A.4)

w ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðu þ c sin fÞ2 þ ðv0 þ sþ c cos fÞ2

q, (A.5)

where w is the total normalized earth-relative wind.In the event that c vanishes, so that the cyclone is stationary, these equations

reduce to the ordinary differential equations:

u _u � sðg þ s�1sÞ þ auw ¼ 0, (A.6)

uð _sþ s�1sþ dÞ þ sðv0 þ sÞw ¼ 0, (A.7)

w ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2 þ ðv0 þ sÞ2

q(A.8)

for the radial profiles u(s) and s(s). Here, ‘‘.’’ indicates differentiation withrespect to s.

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A.3. Wind model implementation

Eqs. (A.3) and (A.4) supplemented by (A.5), constitute two, coupled, timeindependent partial differential equations for the storm relative radial velocity u andthe storm relative departure from gradient balance s. The storm relative tangentialwind is then given by v ¼ vg+s. Unfortunately, the direct numerical solution of (A.3)and (A.4) is time consuming even though the equations are time-independentbecause the non-linear coupling of the terms necessitates an iterative numericalapproach.

However, Eqs. (A.6) and (A.7), can readily be numerically integrated to furnish acompletely symmetric wind field fully described by the radial profiles u(s) andv(s) ¼ vg(s)+s(s).

The functions u(s) and s(s) so obtained can serve as radial profiles for theconstruction of basis functions for a more realistic attack on (A.3) and (A.4).

Namely, we put forth the ansatz:

uðs;fÞ ¼ ffuðfÞuðsÞ, (A.9)

sðs;fÞ ¼ ffsðfÞsðsÞ, (A.10)

where the azimuthal dependence is introduced through the form factors:

ffuðfÞ ¼ a0 þ a1 cos fþ a2 sin f, (A.11)

ffsðfÞ ¼ b0 þ b1 cos fþ b2 sin f. (A.12)

Now the six coefficients a0, a1, a2 and b0, b1, b2 can be variationally determined bysubstituting (A.9) and (A.10) into the left-hand sides of (A.3) and (A.4),supplemented by (A.5) to form the ‘‘residuals’’ RA3 and RA4. We then form thefunctional

Jða; bÞ ¼

PRA3j j þ RA4j j

NGRID, (A.13)

where the sum is taken over every spatial point for which the profiles andtrigonometric functions are known (polar grid) and NGRID is the total number ofsuch grid points.

J then depends solely on the unknown coefficients a0, a1, a2 and b0, b1, b2. Thesecoefficients are chosen to minimize J and so furnish us with an approximate solutionfor u,(s,f) and s(s,f), from which we form the storm relative radial and tangentialwind components ur and vt, namely:

urðs;fÞ ¼ uðs;fÞ and vtðs;fÞ ¼ vgðs;fÞ þ sðs;fÞ, (A.14)

By adding the translational velocity c (in polar coordinates) to ur and vt we obtainthe earth-relative components of the windfield uer and ver:

uerðs;fÞ ¼ urðs;fÞ þ c sin f, (A.15)

verðs;fÞ ¼ vrðs;fÞ þ c cos f, (A.16)

where c is the normalized translation speed c ¼ ct/vgmax.

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Finally, since (A.3), (A.4) and (A.5) refer to a cyclone moving along the Y-axis, theentire generated wind field grid must be rotated so that the Y-axis of the calculationcoincides with the actual compass direction of motion of the translating cyclone.

References

[1] C.J. Neumann, B.R. Jarvinen, C.J. McAdie, G.R. Hammer, Tropical Cyclones of the North Atlantic

Ocean, 1871–1998, National Oceanic and Atmospheric Administration, 1999, 206pp.

[2] L.R. Russell, Probability distributions for hurricane effects, J. Waterways Harbors Coastal Eng. Div.

ASCE 97 (1971) 139–154.

[3] M.E. Batts, M.R. Cordes, L.R. Russell, E. Simiu, Hurricane wind speeds in the United States,

National Bureau of Standards, Report no BSS-124, US Department of Commerce, 1980.

[4] C.W. Landsea, R.A. Pielke Jr., A.M. Mestas-Nunez, J.A. Knaff, Atlantic basin hurricanes: indices of

climatic changes, Climatic Change 42 (1999) 89–129.

[5] B.R. Jarvinen, C.J. Neumann, M.A.S. Davis, A tropical cyclone data tape for the North Atlantic

basin 1886–1963: contents limitations and uses, NOAA Technical Memo NWS NHC 22, National

Hurricane Center, 1984, 22pp.

[6] R.W.R. Darling, Estimating probabilities of hurricane wind speeds using a large scale empirical

model, J Climate 4 (1991) 1035–1046.

[7] R. Rotunno, K.A. Emanuel, An air-sea interaction theory for tropical cyclones, Part II. Part I,

J. Atmos. Sci. 42 (1987) 1062–1071.

[8] H.E. Willoughby, M.D. Shoreibah, Concentric eyewalls, secondary wind maxima, and the evolution

of the hurricane vortex, J. Atmos. Sci. 39 (1982) 395–411.

[9] M.D. Powell, S.H. Houston, Hurricane Andrew’s landfall in South Florida. Part II: surface wind

fields and potential real-time applications, Weather Forecast. 11 (1996) 329–349.

[10] L.K. Shay, G.J. Goni, P.G. Black, Effects of a warm oceanic feature on Hurricane Opal, Mon.

Weather Rev. 125 (5) (2000) 1366–1383.

[11] B.I. Miller, A study on the filling of Hurricane Donna (1960) over land, Mon. Weather Rev. 92 (1964)

389–406.

[12] M.D. Powell, The transition of the Hurricane Frederic boundary layer wind field from the open Gulf

of Mexico to landfall, Mon. Weather Rev. 110 (1982) 1912–1932.

[13] P.J. Vickery, L.A. Twisdale, Wind field and filling models for hurricane wind speed predictions,

. Struct. Eng. 121 (1995) 1700–1709.

[14] F.P. Ho, J.C. Su, K.L. Hanevich, R.J. Smith, F.P. Richards, Hurricane climatology for the Atlantic

and Gulf coasts of the United States, NOAA Technical Memo NWS 38, NWS Silver Spring, MD,

1987.

[15] R.E. Tuleya, M.A. Bender, Y. Kurihara, A simulation study of the landfall of tropical cyclones using

a movable nested-mesh model, Mon. Weather Rev. 112 (1984) 124–136.

[16] J. Kaplan, M. DeMaria, A simple empirical model for predicting the decay of tropical cyclone winds

after landfall, J. Appl Meteorol 34 (1995).

[17] K.V. Ooyama, Numerical simulation of the life cycle of tropical cyclones, J. Atmos. Sci. 26 (1969)

3–40.

[18] L. Shapiro, The asymmetric boundary layer flow under a translating hurricane, J. Atmos. Sci. 40

(1983) 1984–1998.

[19] E.F. Thompson, V.J. Cardone, Practical modeling of hurricane surface wind fields, J. Waterways Port

Coastal Ocean Eng. Div. ASCE 122 (1996) 195–205.

[20] P.J. Vickery, P.F. Skerjl, A.C. Steckley, L.A. Twisdale, A hurricane wind field model for use in

simulations, J. Struct. Eng. 126 (2000) 1203–1222.

[21] P.J. Vickery, P.F. Skerjl, L.A. Twisdale, Simulation of hurricane risk in the United States using an

empirical storm track modeling technique, J. Struct. Eng. 126 (2000) 1222–1237.

[22] Y.M. Kurihara, M.A. Bender, R.E. Tuleya, R.J. Ross, Improvements in the GFDL hurricane

prediction system, Mon. Weather Rev. 123 (1995) 2791–2801.

ARTICLE IN PRESS


[23] G.J. Holland, An analytic model of the wind and pressure profiles in hurricanes, Mon. Weather Rev.

108 (1980) 1212–1218.

[24] H.E. Willoughby, M.E. Rahn, Parametric representation of the primary hurricane vortex Part I:

observations and evaluation of the Holland (1980) model, Mon. Weather Rev. 132 (2004) 3033–3048.

[25] M. Demaria, J. Pennington, K. Williams, Description of the Extended Best track file (EBTRK1.4)

version 1.4, Available from NESDIS/CIRA/Regional and Mesoscale Meteorology Team, Colorado

State University, Fort Collins, CO, 2002.

[26] M.D. Powell, P.J. Vickery, T. Reinhold, Reduced drag coefficient for high wind speeds in tropical

cyclones, Nature 422 (2003) 279–283.

[27] W.G. Large, S. Pond, Open ocean momentum flux measurements in moderate to strong winds,

J. Phys. Oceanogr. 11 (1981) 324–336.

[28] M.S. Moss, S.L. Rosenthal, On the estimation of planetary boundary layer variables in mature

hurricanes, Mon. Weather Rev. 106 (1975) 841–849.

[29] M.D. Powell, Evaluations of diagnostic marine boundary layer models applied to hurricanes,

Mon.Weather Rev. 108 (1980) 757–766.

[30] ASTM, Standard practice for characterizing surface wind using a wind vane and rotating

anemometer, D 5741-96, Annual Book of ASTM Standards, vol. 11.03, 1996.

[31] F. Anctil, M. Donelan, Air–water momentum flux observations over shoaling waves, J. Phys.

Oceanogr. 26 (1996) 1344–1353.

[32] T. Reinhold, K. Gurley, Florida Coastal Monitoring Program, 2003; http://www.ce.ufl.edu/�fcmp.

[33] M.D. Powell, S.H. Houston, T. Reinhold, Hurricane Andrew’s landfall in south Florida. Part I:

standardizing measurements for documentation of surface wind fields, Weather Forecast. 11 (1996)

304–328.

[34] E. Simiu, R.H. Scanlan, Wind Effects on Structures: Fundamentals and Applications to Design,

Wiley, New York, 1996.

[35] E.W. Peterson, Modification of mean flow and turbulent energy by a change in surface roughness

under conditions of neutral stability, Q.J.R. Meteorol. Soc. 95 (1969) 561–575.

[36] H.P. Schmidt, T.R. Oke, A model to estimate the source area contributing to turbulent exchange in

the surface layer over patchy terrain, Q.J.R. Meteorol. Soc. 116 (1990) 965–988.

[37] L.M. Axe, Hurricane surface wind model for risk assessment, M.S. Thesis, Department of

Meteorology, Florida State University, 2003.

[38] J.E. Vogelmann, S.M. Howard, L. Yang, C.R. Larson, B.K. Wylie, N. Van Driel, Completion of the

1990s National land cover data set for the conterminous United States from landsat thematic mapper

data and ancillary data sources, Photogramm. Eng. Remote Sens. 67 (2001) 650–652.

[39] P.J. Vickery, P.F. Skerlj, Hurricane gust factors revisited, J. Struct. Eng. 131 (2005) 825–832.

[40] M.D. Powell, S.H. Houston, I. Ares, Real-time damage assessment in hurricanes, The 21st AMS

Conference on Hurricanes and Tropical Meteorology, Miami, FL, April 24–28, 1995, Paper 12A.4

pp. 500–502.

[41] Commission 2004, Report of Activities as of November 1, 2004, Florida Commission on Hurricane

Loss Projection Methodology, available from www.fsba.state.fl.us/methodology/meetings.asp

http://www.ce.ufl.edu/~fcmp

http://www.ce.ufl.edu/~fcmp

http://www.fsba.state.fl.us/methodology/meetings.asp

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